<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2d1 20170631//EN" "JATS-journalpublishing1.dtd"> <ArticleSet> <Article> <Journal> <PublisherName>ijesm</PublisherName> <JournalTitle>International Journal of Engineering, Science and</JournalTitle> <PISSN>I</PISSN> <EISSN>S</EISSN> <Volume-Issue>Volume 6, Issue 4</Volume-Issue> <PartNumber/> <IssueTopic>Multidisciplinary</IssueTopic> <IssueLanguage>English</IssueLanguage> <Season>August 2017</Season> <SpecialIssue>N</SpecialIssue> <SupplementaryIssue>N</SupplementaryIssue> <IssueOA>Y</IssueOA> <PubDate> <Year>2017</Year> <Month>08</Month> <Day>1</Day> </PubDate> <ArticleType>Engineering, Science and Mathematics</ArticleType> <ArticleTitle>LINEAR AND NONLINEAR ANALYSIS OF THERMAL INSTABILITY IN A POROUS SATURATED BY A NANOFLUID</ArticleTitle> <SubTitle/> <ArticleLanguage>English</ArticleLanguage> <ArticleOA>Y</ArticleOA> <FirstPage>71</FirstPage> <LastPage>89</LastPage> <AuthorList> <Author> <FirstName>Jada Prathap Kumar</FirstName> <LastName>*</LastName> <AuthorLanguage>English</AuthorLanguage> <Affiliation/> <CorrespondingAuthor>N</CorrespondingAuthor> <ORCID/> <FirstName>Jawali Channabasappa Umavathi** and Channakeshava</FirstName> <LastName>Murthy***</LastName> <AuthorLanguage>English</AuthorLanguage> <Affiliation/> <CorrespondingAuthor>Y</CorrespondingAuthor> <ORCID/> </Author> </AuthorList> <DOI/> <Abstract>In this present article, the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is investigated analytically using linear and weakly nonlinear analysis. The model used for the nanofluid incorporates the effect of Brownian motion and thermophoresis. The effect of Raleigh-Darcy number, Lewis Number, modified diffusivity ratio, Vadasz number and normalized porosity parameter on the stability of the system is investigated .The analysis reveals that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via buoyancy effect coupled with the conservation of nanoparticles to the thermal energy equation being a second –order effect. Stationary and oscillatory modes of convections have been studied. It is found that the critical thermal Raleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy, by the presence of the nanoparticles .Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution. The linear stability analysis is based on normal mode technique, while for nonlinear theory is based on the truncated representation of Fourier series method. A weakly nonlinear analysis is used to obtain the concentration and thermal Nusselt number. The behavior of the concentration and thermal Nusselt numbers is investigated by a solving the finite amplitude equations. Obtained results have been presented graphically and discussed in details.</Abstract> <AbstractLanguage>English</AbstractLanguage> <Keywords>Nanofluid, Porous medium, Instability, Natural convection.</Keywords> <URLs> <Abstract>https://ijesm.co.in/ubijournal-v1copy/journals/abstract.php?article_id=3290&title=LINEAR AND NONLINEAR ANALYSIS OF THERMAL INSTABILITY IN A POROUS SATURATED BY A NANOFLUID</Abstract> </URLs> <References> <ReferencesarticleTitle>References</ReferencesarticleTitle> <ReferencesfirstPage>16</ReferencesfirstPage> <ReferenceslastPage>19</ReferenceslastPage> <References/> </References> </Journal> </Article> </ArticleSet>